The Mass of Asymptotically Hyperbolic Manifolds

By Xiaodong Wang. 2001

281 citations recorded by the source corpus.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8591c9733f1386e4185f07793ab3f195e127e06b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. A. Neves
2. F. C. Marques
3. M. Mars
4. Ivaldo Nunes
5. Antoine Song
6. M. Li
7. P. Hintz
8. G. Galloway

In Astronomy and Astrophysics

1. F. C. Marques
2. P. Hintz
3. G. Galloway
4. A. Neves
5. G. Tian
6. Ivaldo Nunes
7. András Vasy
8. Yuguang Shi

In Geometry and Topology

1. A. Neves
2. F. C. Marques
3. Ivaldo Nunes
4. Antoine Song
5. M. Li
6. P. Hintz
7. G. Galloway
8. G. Tian

Citations in the corpus

• The global non-linear stability of the Kerr-de Sitter family of black holes (2016, methodology): “Investigating any such method, potentially via making a connection to different notions of mass on asymptotically hyperbolic manifolds [144], [150], [27], [20], would be a very interesting problem.”
• Present status of the Penrose inequality (2009, background): “In the case when the boundary at infinity ∂Σ is a two-sphere, the definition was first given in [163].”
• Rigidity of Asymptotically Hyperbolic Manifolds (2004, result): “In [7], using the Dirac operator, Min-oo proved that a spin manifold of dimension n must be a hyperbolic space if it is asymptotic to hyperbolic space in a strong sense and its scalar curvature is not less that −n(n − 1). His argument was refined and new exciting results were obtained by Andersson a”
• Rigidity of Area-Minimizing Hyperbolic Surfaces in Three-Manifolds (2011, background): “There are some analogous rigidity results for the hyperbolic space (see [19], [2], [9] and [27]).”
• The Penrose Inequality for Asymptotically Locally Hyperbolic Spaces with Nonpositive Mass (2013, unknown): “Herzlich [7] and by Wang [19], for the case of a manifold with minimal (1)Although we are unable to replace m̄ by m in general, we do obtain a slightly stronger inequality than (1).”
• Insufficient convergence of inverse mean curvature flow on asymptotically hyperbolic manifolds (2007, methodology): “The main purpose of this paper is to show that, contrarily to what was suggested in [13], the inverse mean curvature flow does not have the necessary convergence properties in order to prove this conjecture.”
• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds (2007, methodology): “More recently, Wang [26], and, under weaker asymptotic conditions, Chruściel and Herzlich [10] have provided precise definitions of the mass in the asymptotically hyperbolic setting and have given spinor based proofs of positivity of mass in dimensions ≥ 3.”
• Rigidity of min-max minimal spheres in three-manifolds (2011, background): “The search for scalar curvature rigidity results for the standard sphere is motivated by the Positive Mass Theorems in both the Euclidean ([32], [41]) and the hyperbolic ([9], [38], see also [2], [22]) settings.”